Behind the courtroom conflict that has left Argentina in default lies an expensive international lobbying campaign designed to win the hearts, minds and votes of those who could influence the outcome of the decade-long dispute between the Argentine government and a powerful group of hedge funds.

The fight accelerated this summer when the U.S. Supreme Court declined to consider overturning lower court rulings requiring Argentina to pay bondholders who had refused to accept the country’s debt restructuring offer after a 2001 default. Those holdouts, mostly U.S.-based hedge funds, represent just 7 percent of Argentina’s bondholders, but the tussle has consumed the country’s psyche and an arsenal of well-paid lawyers, leading to Twitter wars and international pleas for support.

While the courtroom disputes have been very public, another part of the battle has been waged behind the scenes by high-powered lobbyists and consultants on private missions from Buenos Aires and Washington.

Both sides are attempting not just to reach government officials who could influence the case but to shape public sentiment as well.

The scope of their work has spilled into public view recently, with dueling full-page newspaper ads appearing in major newspapers around the globe and a cascade of ads posted to online sites.

“They [the hedge funds] purchased bonds in default at obscenely low prices for the sole purpose of engaging in litigation against Argentina and making enormous profit,” reads a full-page ad commissioned by the Argentine government that attacks the hedge fund plaintiffs, who are labeled “vultures” by Argentine officials and their allies.

Since the Supreme Court declined to consider the matter, the color display ads have run repeatedly in The Washington Post, the New York Times, the Wall Street Journal and other major papers around the globe. Versions have shown up in El País (Spain), the Financial Times (England), the Frankfurter Allgemeine Zeitung (Germany) and Le Monde (France).

And these ads have been answered by full-page advertisements from American Task Force Argentina, a nonprofit group partly funded by the hedge funds that have brought suit against Argentina. One ad placed in a prominent newspaper a few weeks ago declared: “Argentina, Default is Your Choice. It’s Time to Negotiate.”

Last year, the group published stinging descriptions of Argentina. “It’s Time for Argentina to Obey U.S. Law and Stop Disrespecting U.S. Courts,” said one ad. Another 2013 advertisement bashed Argentina for having “shameful allies,” including Iran.

ATFA, Argentina’s embassy and Elliott Management, the hedge fund that has led the lawsuit against Argentina over the debt payments, all declined to comment for this article.

It is impossible to know how much either side has spent on the campaigns. But full-page newspaper ads such as these can run from $80,000 to several hundred thousand dollars each, according to advertising consultants and news industry executives. And there have been dozens published in recent weeks.

ATFA has also unleashed high-profile lobbyists.

This month, ATFA spokespersons Nancy Soder­berg, a senior official during Bill’s Clinton presidency and a foreign policy adviser to former New York mayor Michael Bloomberg, and Robert Shapiro, undersecretary of commerce for economic affairs in the Clinton administration and an economic adviser to Al Gore and John Kerry in their campaigns, traveled to Buenos Aires to “caution against the default, pointing out the misinformation” coming from the Argentine side, as Shapiro put it.

And the Argentine government has shown it can deploy unconventional means to disperse its message in Washington. In June, for instance, the government hosted a seminar on the debt dispute in a hearing room in the Capitol Visitor Center, an unlikely venue for a foreign government to make its case.

A few weeks before a key court ruling in the case in 2012, Argentine government officials had the opportunity to make their case directly to their U.S. counterparts, meeting with top Democratic and Republican lawmakers and party officials in Washington.

The visiting Argentines toured the White House and the Capitol and, during a visit to the U.S. Supreme Court, met Justice Sonia Sotomayor. Sotomayor brushed off a question about the pending legal dispute, according to Eduardo Antonio Diez, the executive director of an Argentine foundation, and several others in attendance who asked not to be named.

Sotomayor was not available for comment.

At about the same time, in Buenos Aires, 25 members of the U.S. Congress met with government and opposition politicians. The Americans’ meetings included sessions with top Argentine legislators and Cabinet officials, and they even met with the president.

And Argentina’s high level lobbying has continued. Since the July Supreme Court decision, Argentine President Cristina Fernández de Kirchner has traveled to Venezuela and Brazil to actively seek support from other countries.

In addition, Fernández has sought to whip up support at home. Her office produced a video that aired on Argentine television and featured spokespersons from Brazil, Uruguay, Peru, Mexico, Paraguay, Honduras, Colombia and Bolivia supporting the government’s position.

It’s unclear whether either side has succeeded substantially in changing minds in the case. In Argentina, officials deny the country has defaulted, even though Standard & Poor’s declared a “technical” default last week after Argentina missed a deadline to pay debt holders.

“Some say our world is falling apart,” Fernández said in a speech Monday, “but we will keep on working. If we make mistakes, it is because we work. . . . Here we are to bite the bullet, as we have always done in hard times.”